NON-AUTONOMOUS STOCHASTIC EVOLUTION EQUATIONS, INERTIAL MANIFOLDS AND CHAFEE-INFANTE MODELS

• Tác giả: Van Loi Do, Anh Minh Le
• Ngôn ngữ: vie
• Thông tin xuất bản: Hong Duc University Journal of Science, 2019
• Bộ sưu tập: Metadata
• ID: 389490

Tóm tắt

 Consider a stochastic evolution equation containing Stratonovich-multiplicative white noise of the formwhere the partial differential operatoris positive definite, self-adjoint with a discrete spectrum
  and the nonlinear partsatisfies the-Lipschitz condition withbelonging to an admissible function space. We prove the existence of a (stochastic) inertial manifold for the solutions to the above equation. Our method relies on the Lyapunov-Perron equation in a combination with the admissibility of function spaces. An application to the non-autonomous Chafee - Infante equations is given to illustrate our results.